I have written a small article comparing the performance of Mono (version 1.1.8.3) and that of the .NET Framework (v1.1 SP1). The results are rather surprising, the two running side by side with no clear winner.
Mono vs. .NET Performance Test
UPDATE:
John Tertin has made some more through tests comparing Mono to .NET 2.0. A lot seems to have changed :). You can download the results
here.